Quantum state space is foliated into minimum-variance leaves via quantum Fisher information to define leaf-canonical ensembles that incorporate coherence and support a leaf typicality hypothesis extending eigenstate thermalization.
Quantum Fisher Information as the Convex Roof of Variance
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Quantum Fisher information places the fundamental limit to the accuracy of estimating an unknown parameter. Here we shall provide the quantum Fisher information an operational meaning: a mixed state can be so prepared that a given observable has the minimal averaged variance, which equals exactly to the quantum Fisher information for estimating an unknown parameter generated by the unitary dynamics with the given observable as Hamiltonian. In particular we shall prove that the quantum Fisher information is the convex roof of the variance, as conjectured by Toth and Petz based on numerical and analytical evidences, by constructing explicitly a pure-state ensemble of the given mixed state in which the averaged variance of a given observable equals to the quantum Fisher information.
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A resource theory for strong symmetry breaking is formulated, with the variance of the conserved quantity characterizing its asymptotic manipulation for U(1) symmetry and enabling tracking of weak-to-strong conversion in open systems.
Covariance matrices for finite-dimensional DFT-related position-momentum pairs are fully characterized via unitary invariants, convex geometry, and SDP, yielding extremal states and application bounds.
Entanglement asymmetry for inhomogeneous U(1) charges in fragmented systems scales extensively, is bounded by a universal fraction of its maximum, and distinguishes classical from quantum fragmentation.
Coherent enhancement in detectors is quantitatively constrained by single-mode entanglement entropy, with general bounds on scaling with system size that interpolate between incoherent and fully coherent regimes.
A method is given to compute the minimum energy of certain spin Hamiltonians over separable states, expressed via quantum Fisher information for Ising models and fidelity for Heisenberg chains.
Derives QSLs based on square roots of Jensen-Shannon and Jeffreys divergences, expressed via Schatten speed and eigenvalue cost functions, for general quantum processes including unitary evolution and specific open channels.
Proves equalities among quantum Wasserstein distances obtained from optimizations over general versus separable bipartite states and shows relations to Uhlmann-Jozsa fidelity and superfidelity, including equality for qubits.
citing papers explorer
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Quantum-Coherent Thermodynamics: Leaf Typicality via Minimum-Variance Foliation
Quantum state space is foliated into minimum-variance leaves via quantum Fisher information to define leaf-canonical ensembles that incorporate coherence and support a leaf typicality hypothesis extending eigenstate thermalization.
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Resource-Theoretic Quantifiers of Weak and Strong Symmetry Breaking: Strong Entanglement Asymmetry and Beyond
A resource theory for strong symmetry breaking is formulated, with the variance of the conserved quantity characterizing its asymptotic manipulation for U(1) symmetry and enabling tracking of weak-to-strong conversion in open systems.
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The uncertainty geometry of finite-dimensional position and momentum
Covariance matrices for finite-dimensional DFT-related position-momentum pairs are fully characterized via unitary invariants, convex geometry, and SDP, yielding extremal states and application bounds.
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Enhancing entanglement asymmetry in fragmented quantum systems
Entanglement asymmetry for inhomogeneous U(1) charges in fragmented systems scales extensively, is bounded by a universal fraction of its maximum, and distinguishes classical from quantum fragmentation.
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Entanglement Requirements for Coherent Enhancement in Detectors
Coherent enhancement in detectors is quantitatively constrained by single-mode entanglement entropy, with general bounds on scaling with system size that interpolate between incoherent and fully coherent regimes.
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General method for obtaining the energy minimum of spin Hamiltonians for separable states
A method is given to compute the minimum energy of certain spin Hamiltonians over separable states, expressed via quantum Fisher information for Ising models and fidelity for Heisenberg chains.
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Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
Derives QSLs based on square roots of Jensen-Shannon and Jeffreys divergences, expressed via Schatten speed and eigenvalue cost functions, for general quantum processes including unitary evolution and specific open channels.
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Quantum Wasserstein distance and its relation to several types of fidelities
Proves equalities among quantum Wasserstein distances obtained from optimizations over general versus separable bipartite states and shows relations to Uhlmann-Jozsa fidelity and superfidelity, including equality for qubits.